Challenges of bibliometric mapping and scattering analysis and interpretations

By Avishek Majumder on April 10, 2018

The previous article speaks of challenges of selection of software and data analysis in a bibliometric study. Challenges of bibliometrics arise at every checkpoint of bibliometrics. Thus, the last section of the bibliometric analysis comprises of challenges with respect to mapping and scattering analysis. Moreover, the challenges also comprise of interpretation from data analyses of mapping and scattering.

The process of bibliometrics
The process of bibliometrics

Mapping analyses

Mapping analyses or network analyses, present linkage between two or more authors, keywords, citations and other information related bibliography who had authored or were a part of the journal (Eck, Waltman, Dekker, & Berg, 2010). Thus, mapping analysis presents the relation between citations to form a series of network and maps. Network analysis, on the other hand, comprises of co-occurrence of keywords, co-authorship pattern, co-citation pattern and co-occurrence of subjects.

Mapping and networking sample analysis
Mapping and networking sample analysis

Challenges of interpretations for mapping analyses

In the initial stages of interpreting the findings of mapping or network analysis, the most important challenge faced is differentiating cluster and sub-clusters. Thus, clusters are basically concentration of the texts, word or author name or citation that have direct links to another set of texts, word or author name or citation. In the image above, the text ‘humans’ form the initial cluster (largest cluster), linked to each and every other sub-groups or clusters directly or indirectly.

Furthermore, every mapped bibliometric data has a large cluster and smaller clusters. Larger clusters indicate higher linkage or co-occurrence or repetition of the text or citations. The smaller clusters get the lower linkage of the text or the citations are to other texts with respect to co-occurrence or repetition. Identification of clusters is a big challenge while interpreting the findings of bibliometric mapping. Another challenge is, failing to interpret the centralization of clusters. The cluster to the center is the most repetitive or occurred texts, word or author name or citation. The clusters farthest are usually smaller in size and have least repetitive texts, word/author name or citation.

Points to remember

  1. Clusters represent repetitive or occurred texts, word or author name or citation from co-occurrence, co-citations and co-authorship analyses.
  2. Clusters centralized in the zone are different to the size of the clusters, with respect to repetitive texts, word or author name or citation, although both present repetitive texts, word or author name or citation.
  3. Smaller clusters condensed to the central zone may have less number or repetitive texts, word or author name or citation and may still be present in the central zone of bibliometric map. This is because, the particular cluster belongs to most condensed group or cluster.
  4. Lastly, the size of cluster indicates the number or repetitive texts, word/author name or citation only.

Challenges of interpretations for scattering analyses

Scattering analyses comprise of Bradford law of scattering, that shows the pattern or the scattering of the particular subject in the journals (Huang et al., 2014). However, there are basically three laws of bibliometrics, which are Bradford’s law, Lotka’s Law and Zipf’s Law. Frequency of publication is given by Lotka’s Law, while frequency of appearance or occurrence is given by Zipf’s Law. Scattering analysis is however most commonly used for distribution of literature. However, other analyses of Bradford comprise of frequency and percentage of presence of published articles in other journals.

Representation of Bradford law of scattering
Representation of Bradford law of scattering

One of the most important challenge in assessing Bradford’s law of scattering is that, open source software are not available. Automated software, thus, provide limited access or paid access. Similarly, another challenge is that, manual calculation of scattering is time taking and may face many mathematical mistakes. Lastly, another challenge is the selection of formula. First, verbal formulation comprises of decreasing number of frequency of citations. On the other hand, second graphical formulation comprise of empirical expression based on distribution of periodicals and given by 1:n:n2.

Points to remember

  1. Verbal formula is the best way to ignore mathematical errors.
  2. Furthermore, the zones must have geometric series in the form 1:n:n 2; else publications and citation does not fit into the Bradford’s distribution.
  3. Lastly, the formula in sequence used for Bradford’s Law of Scattering and represent in verbal comprise of:
    • Linear relation to describe the scattering phenomenon using: F(x) = a + b log x.
    • F(x): cumulative number of references and x most productive journals and “a” and “b” are constants.
    • Values for a and b: a = Ya /log k and b = k-1/r0; is the number of sources in the first Bradford’s group, Ya is the number of items in every Bradford group and k is the Bradford multiplier.
    • Y0=A/P; A denotes the total number of articles and P is 3 for 3 zones.
    • Bradford multiplier k, k = (e γ y m ) 1/p; Where g is Euler’s number (1.781) and y m is the number of items.
    • r0= number of journals in the nucleus of Bradford is calculated; r 0 = T (k-1)/(k P -1); T = Total number of Journals, and k is Bradford multiplier.
    • Bradford Zones 1:n:n 2; where, Nucleus zone 1= r0 = r0 x 1, First zone 2= r0 x k and Second zone 3= r0 x k 2.

Thus, following the formula as above presents fitting of citation in Bradford’s distribution and imply that there is or no relationship or link between the journals published.

Key notes

  1. Assessment of field of study and publication target.
  2. Usage and identification of appropriate source for data collection.
  3. Application of appropriate software on the basis of analyses chosen and formats availability.
  4. Usage of appropriate analytics.
  5. Finally, rightful application of mathematical formulas and adequate interpretations of the data analysed.

Henceforth, the 5 rules are very important for appropriate and effective Bibliometric analyses, specially with constraints of data collection and availability of information.


  • Eck, N. V. J., Waltman, L., Dekker, R., & Berg, J. Van Den. (2010). A comparison of two
    techniques for bibliometric mapping: Multidimensional scaling and VOS. Journal of the
    American Society for Information Science and Technology, 61(12), 2405–2416.
  • Huang, M. H., Huang, W. T., Chang, C. C., Chen, D. Z., & Lin, C. P. (2014). The greater
    scattering phenomenon beyond bradford’s law in patent citation. Journal of the Association
    for Information Science and Technology, 65(9), 1917–1928.